Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Tangent bundles to regular basic sets in hyperbolic dynamics


Author: Luchezar Stoyanov
Journal: Proc. Amer. Math. Soc. 140 (2012), 1623-1631
MSC (2010): Primary 37D20, 37D40
Published electronically: August 18, 2011
MathSciNet review: 2869147
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a locally maximal compact invariant hyperbolic set $ \Lambda$ for a $ C^2$ flow or diffeomorphism on a Riemann manifold with $ C^1$ stable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable manifolds that locally approximates $ \Lambda$ in a certain way.


References [Enhancements On Off] (What's this?)

  • [B] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429-460. MR 0339281 (49:4041)
  • [Ch] N. Chernov, Invariant measures for hyperbolic dynamical systems, in: Handbook of Dynamical Systems, ed. by A. Katok and B. Hasselblatt, Vol. 1A, pp. 321-407, North-Holland, Amsterdam, 2002. MR 1928521 (2003g:37047)
  • [D] D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (2) 147 (1998), 357-390. MR 1626749 (99g:58073)
  • [GP] V. Guillemin and A. Polack, Differential topology, Prentice Hall, New Jersey, 1974. MR 0348781 (50:1276)
  • [Ha] B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergod. Th. & Dynam. Sys. 14 (1994), 645-666. MR 1304137 (95j:58130)
  • [Ka] M. Kapovich, Kleinian groups in higher dimensions, Progress in Mathematics, Vol. 265, Birkhäuser Basel, 2008, 485-562. MR 2402415 (2009g:30043)
  • [KH] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge Univ. Press, Cambridge, 1995. MR 1326374 (96c:58055)
  • [M] B. Malgrange, Ideals of differentiable functions, Oxford University Press, 1966. MR 0212575 (35:3446)
  • [PSW] C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J. 86 (1997), 517-546; Correction: Duke Math. J. 105 (2000), 105-106. MR 1432307 (97m:58155); MR 1788044 (2001h:37057)
  • [Ratc] J. G. Ratcliffe, Foundations of hyperbolic manifolds, Springer-Verlag, New York, 1994. MR 1299730 (95j:57011)
  • [St1] L. Stoyanov, Exponential instability and entropy for a class of dispersing billiards, Ergod. Th. & Dynam. Sys. 19 (1999), 201-226. MR 1677157 (99m:58149)
  • [St2] L. Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity 24 (2011), 1089-1120.
  • [St3] L. Stoyanov, Non-integrability of open billiard flows and Dolgopyat type estimates, Ergod. Th. & Dynam. Sys., to appear, doi:10.1017/S0143385710000933.
  • [St4] L. Stoyanov, Pinching conditions, linearization and regularity of Axiom A flows, preprint (arXiv: math.DS:1010.1594).
  • [Su] D. Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), 259-278. MR 766265 (86c:58093)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37D20, 37D40

Retrieve articles in all journals with MSC (2010): 37D20, 37D40


Additional Information

Luchezar Stoyanov
Affiliation: School of Mathematics, University of Western Australia, Crawley, WA 6009, Australia
Email: stoyanov@maths.uwa.edu.au

DOI: https://doi.org/10.1090/S0002-9939-2011-11001-3
Received by editor(s): July 28, 2010
Received by editor(s) in revised form: November 27, 2010, and January 10, 2011
Published electronically: August 18, 2011
Additional Notes: The author thanks the referee for useful comments and suggestions.
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.